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Izv. RAN. Ser. Mat., 2012, Volume 76, Issue 3, Pages 19–38 (Mi izv6283)  

This article is cited in 9 scientific papers (total in 9 papers)

The discrepancy of the Korobov lattice points

V. A. Bykovskii

Institute for Applied Mathematics, Khabarovsk Division, Far-Eastern Branch of the Russian Academy of Sciences

Abstract: We obtain substantially improved bounds for the discrepancy of the Korobov lattice points from the uniform distribution.

Keywords: uniform distribution, Korobov lattice points, lattice, relative minimum.

DOI: https://doi.org/10.4213/im6283

Full text: PDF file (565 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2012, 76:3, 446–465

Bibliographic databases:

UDC: 519.644.7+511.9
MSC: Primary 41A55; Secondary 11K38
Received: 07.12.2010
Revised: 03.03.2011

Citation: V. A. Bykovskii, “The discrepancy of the Korobov lattice points”, Izv. RAN. Ser. Mat., 76:3 (2012), 19–38; Izv. Math., 76:3 (2012), 446–465

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. D. M. Ushanov, “Bykovskii's Theorem and a Generalization of Larcher's Theorem”, Math. Notes, 91:5 (2012), 746–750  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. A. A. Illarionov, “O statisticheskikh svoistvakh lokalnykh minimumov tselochislennykh reshetok”, Dalnevost. matem. zhurn., 12:2 (2012), 201–230  mathnet
    3. A. V. Ustinov, “Minimal Vector Systems in 3-Dimensional Lattices and Analog of Vahlen's Theorem for 3-Dimensional Minkowski's Continued Fractions”, Proc. Steklov Inst. Math., 280, suppl. 2 (2013), S91–S116  mathnet  crossref  crossref  zmath  isi  elib
    4. A. A. Illarionov, “On the statistical properties of Klein polyhedra in three-dimensional lattices”, Sb. Math., 204:6 (2013), 801–823  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. A. A. Illarionov, “A multidimensional generalization of Heilbronn's theorem on the average length of a finite continued fraction”, Sb. Math., 205:3 (2014), 419–431  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. J. Dick, A. Hinrichs, F. Pillichshammer, “Proof techniques in Quasi-Monte Carlo theory”, J. Complexity, 31:3 (2015), 327–371  crossref  mathscinet  zmath  isi  scopus
    7. A. A. Illarionov, “Some properties of three-dimensional Klein polyhedra”, Sb. Math., 206:4 (2015), 510–539  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    8. A. V. Ustinov, “Three-dimensional continued fractions and Kloosterman sums”, Russian Math. Surveys, 70:3 (2015), 483–556  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. O. Karpenkov, A. Ustinov, “Geometry and combinatoric of Minkowski–Voronoi 3-dimensional continued fractions”, J. Number Theory, 176 (2017), 375–419  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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